Since 2003, the team has made tens of millions of dollars on the sales, while paying a tiny fraction in license fees. Now, with the deal set to expire at the end of this season, the club is pushing to make the lucrative arrangement permanent, according to a November letter from the Sox to the Boston Redevelopment Authority that the Globe obtained through a public records request.

In the letter, the Red Sox argue that the low license fee is reasonable because John W. Henry’s ownership group has paid $56.7 million in property, sales, and meals taxes since buying the team in 2002.

The Sox are a “pretty good corporate citizen,” said Victor Matheson, a sports economist at the College of the Holy Cross, but the public street license is an example of how the club “punches above its weight” in Boston, exerting greater influence than countless other tax-paying businesses.

“It’s not obvious why the Red Sox should get special consideration for doing what everyone else does, including mom-and-pop stores,” Matheson said. “You shouldn’t get any great credit for doing your civic duty, right?”

In partnership with the Northeastern University Initiative for Investigative Reporting, the Globe reported in 2011 that the BRA had charged the Red Sox an average of just $186,000 per year for use of the streets, even as Yawkey and Lansdowne generated an estimated $5 million in annual revenues.

Since the Green Monster section opened, the Red Sox have more than tripled seat prices there. Yet the team’s license fee has increased by just 28 percent over the same period — limited by a 5 percent annual cap built into the current contract. In years when the local consumer price index climbs by less than 5 percent, the Red Sox fee goes up by the lower rate.

At the time of the first Globe report, which prompted an inquiry from the state inspector general’s office, BRA director Peter Meade said he would insist in the next round of negotiations that the fee be increased and tied to income earned on the streets, rather than the consumer price index.

Meade declined through a spokeswoman to repeat that public stance on Wednesday, saying he did not want to negotiate through the press.

“But, of course, we’re going to try to get the best deal we can for the city and for taxpayers,” said the spokeswoman, Susan Elsbree.

The Red Sox declined to comment beyond the position outlined in their letter to the BRA.

In the letter, the Red Sox pushed for a permanent extension of the current terms, arguing that a higher fee would represent an “unwarranted, punitive burden” on an ownership group that has never sought public financing for Fenway Park renovations or for a new stadium.

Over the last two decades, Red Sox vice president David S. Friedman noted in the letter to Meade, 22 of 30 Major League clubs have built new ballparks with at least some public dollars.

“In light of the universal practice regarding public support for baseball stadium development, it is certainly appropriate for us to arrive at a permanent extension of our current rights and practices,” Friedman wrote.

While Red Sox owners have spent $285 million on ballpark improvements without public funding, they also have enjoyed
substantial tax breaks that helped to defray their costs. The Massachusetts Historical Commission has awarded the club $47.7 million in tax credits, public records show, and Fenway Park’s inclusion last year on the National Register of Historic Places was worth another $45.4 million in federal tax credits, according to an estimate provided by the National Park Service.

In addition to the profits they reap by doing business on Yawkey and Lansdowne, Red Sox owners could gain another financial benefit by setting their BRA agreement in stone. Granted permanent control of the two streets, owners could claim the license as a capital asset, instead of as an expense, if they were to sell the team.

Such a financial maneuver would increase the team’s net worth, said David C. Morganelli, a tax accountant and lawyer who specializes in mergers and acquisitions.

The Green Monster section — 269 seats and 100 standing-room-only positions — is not contained within Fenway Park but overhangs Lansdowne Street. It is supported by steel columns driven deep into the ground under a public sidewalk.

The license granting the Red Sox air rights over Lansdowne is unusual in that it benefits a single, private entity. Air rights over public roads in Boston have typically been leased to developers planning projects with broader economic impacts.

Ticket price increases have made perches on top of Fenway’s left-field wall some of the most expensive nonluxury suite seats in all of baseball. The section now generates $3.9 million in gross ticket sales over the course of a season. Additional game day spending by fans on food, drink, and souvenirs enhances the Red Sox’s bottom line further.

On the section of Yawkey Way abutting Fenway Park, which the Sox are permitted to close to vehicles before each of the 81 home games, gross sales for concessions totaled $2 million last season and have been significantly higher in other years, the club reported in its letter to the BRA.

Yawkey Way concession revenue appears likely to rise in the future because the team’s competitors — 18 private vendors with permits to sell food and drink around the ballpark — are being gradually phased out by the city. As the current permit holders retire or die, the city will not allow other vendors to replace them, CommonWealth magazine reported in January.

The Red Sox minimized the revenue potential of Yawkey Way in their letter, claiming that the street is not a major source of profit because the team splits the money with its concession provider, Aramark Corp., and Major League Baseball. The street’s closure on game days is primarily about “public safety and improved fan comfort,” Friedman wrote.

Even as they lobbied for a permanent extension of the current license terms, the Red Sox asserted that losing Yawkey Way would be no great blow because most of the sales that occur on the street merely substitute for purchases that would otherwise be made inside Fenway.

“If the Red Sox ceased serving patrons on Yawkey Way and instead limited all concessions to inside the ballpark, we expect that we would experience roughly the same overall total concessions sales for ballgames and other Fenway Park events with little, if any, reduction in revenues,” Friedman wrote.